Progressively censored schemes, in which experimentation is continually monitored from the onset, are advocated in some clinical trials and life testing problems with a view to early termination of the experiment, whenever feasible, and concomitant reduction in cost, time and sacrifice of lives of experimental subjects. We investigate the properties of several time sequential statistics (eg. likelihood ratio statistics, occurrence-exposure rates) in this framework together with various stopping mechanisms that are of practical interest. A unified approach is taken for estimation of the survival function under different forms of censoring and some sequential procedures developed for estimation and hypothesis testing problems.